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Plasma Jet Drivers for Magneto-Inertial Fusion (PJMIF)

F. Douglas Witherspoon

HyperV Technologies Corp., Chantilly, VA

with input from Jason Cassibry (UAHuntsville), Scott Hsu (LANL), Francis Thio (DOE )

ARPA-E Workshop

“Drivers For Low-Cost Development Towards Economical Fusion Power”

Berkeley, CA, October 29-30, 2013

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Talk focuses on recent technical achievements that establish the foundationfor a reactor-grade plasma gun driver.

Talk Outline

• Background/History

• Contoured gap coax guns (A new approach)

• Minirailgun injectors

• Minirailgun plasma guns

• Multi-jet technology demonstrations (argon)

• Mark2 Minirailgun performance achievement

• A reactor-grade coax gun system

Baseline use of plasma gun array.

Thio, Y. C. F., C. E. Knapp, R. C. Kirkpatrick, R. E. Siemon,and P. J. Turchi, “A physics exploratory experiment on plasma linerformation,” Journal Fusion Energy, 20(1/2):111 (2001).

S. C. Hsu, T. J. Awe, S. Brockington, A. Case, J. T. Cassibry,G. Kagan, S. J. Messer, M. Stanic, X. Tang, D. R. Welch, and F.D. Witherspoon, “Spherically Imploding Plasma Liners as a StandoffDriver for Magnetoinertial Fusion,” IEEE Transactions On PlasmaScience, Vol. 40, No. 5, May (2012).

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Pulsed plasma accelerator history

• Production of high velocity plasma jets motivated extensive research in

pulsed coaxial plasma accelerators

• Bulk of research conducted in 1960’s

• Early emphasis on understanding acceleration mechanisms, particle ve-

locity distribution, neutron production, and instabilities

• Applications in 1970’s-present

– Fueling of magnetically confined plasmas

– Propulsion

– Dense plasma focus

– Lethal intercept of missiles

• Various modes of operation identified and sensitive to initial conditions

– Mass loading (gas puff, static prefill, preionization)

– Charging voltage, current, capacitance

– Electrode geometry (radius ratio, tapering, inner/outer electrode lengths)

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Milestones Reached in Coaxial Gun Experiments

• Propulsion community placed emphasis on efficiency

– >50% efficiency possible with carefully matched electrode geome-

try, propellant loading, and low inductance driver circuit (Gloresen

et al 1966)

– Mass per pulse ∼10 µg at 10 km/s

• Fusion and weapons communities focused on high veloc-

ities and particle densities

– >200 km/s achievable with high currents (>100 kA)

– Many experiments pursuing high density jets found tapered ge-

ometries desirable (Turchi 1988, Cheng 1971, Komel’kov 1977)

– Mass up to 200 µg

– Collimated jets possible with electrode tapering

• Tokamak fueling focuses on high dynamic pressure

(ρv2 ∼100 bar) and high velocities

– >500 km/s velocities

– Penetration of 5 T toroidal magnetic fields

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HyperV Guns leverage 5 decades of research

• Total particle density and mass ∼an order of magnitude above previous

experiments in new collision dominated regime (Thio et al 2002)

– Earlier research at lower densities shows higher prefill pressures lead to impermeable

current sheet (Komel’kov et al 1977)

• Required velocity well within demonstrated capabilities (numerous

sources)

• >50% efficiencies within reach with impedance matched electrodes and

high utilization efficiency, and thruster staging or preionization (Gloresen

et al 1966)

• Collimated, focused plasma jets produced with electrode taper (Turchi

1988, Chen 1971, Komel’kov et al 1977)

• Cassibry and Thio looked at ways to suppress the blowby instability using

a contoured gap (Cassibry 2006)

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A 2002 paper∗ by Thio proposed a new physics approach to overcome decadesof stagnant progress in classical straight coax guns – thus providingthe key to extremely high performance guns.

Core concepts of the new microphysics

• No prefill gas

• Inject high velocity dense plasma

• High density =⇒ highly collisional

• Taper electrodes to improve flow con-trol

∗Y.C.F. Thio, J.T. Cassibry, and T.E. Markusic, “Pulsed Electromagnetic Acceleration of Plasmas,” AIAA Joint Prop. Conf.,Indianapolis, IN, Paper AIAA-2002-3803, July (2002).

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The Blowby Instability limits performance of a classical straightcoaxial accelerator

*From R.G. Jahn, “Physics of Elec-tric Propulsion,” 1st ed., New York,McGraw-Hill, 1968.

• B ∼ 1/r

• higher J×B near inner electrode

• current distribution is unstable

• J(r, z) “runs away” leaving most mass behind

• must peak density profile near inner electrode

Outer Electrode

Inner Electrode

Outer Electrode

CL

b

b

Hot, Low Density

Plasma Races AheadAlong Inner Electrode

Cool, High Density

Plasma Lags

Behind

Lorentz ForceStrongest Near Axis,⊥ to Current

*Cassibry 2006

Mach2 mass density contour plots illustrate the blow-by in-stability in a straight coaxial accelerator.*

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Electrode profile tailoring suppresses blow-by instability by matching localdensity with local JxB. Curvature forces density peaking along inner wall.

Radius, m

-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20

Z, m

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7CL

The forward tilting of the plasmaincreases in this region, furthercompressing the plasma towardsthe axis. The conical z-pinch withthe vertex at F propels the plasmaforward as a focused or a wellcollimated jet.

The plasma expands and acceleratesaround the inner electrode. MajorLorentz acceleration continues withforward tilting of the current beginningto focus the flow electromagnetically.

The outward curvature of the innerelectrode further prevents theoccurrence of blow-by.

The curvature of the electrode herebends the supersonic plasma flowinto itself, compressing it, forminga denser plasma along the innerelectrode. It also creates a longerpath along the inner electrode.

The plasma expandssupersonically around the outerelectrode, giving rise to reduceddensity along the outer electrode,and gets ahead of the plasma atthe inner electrode.

Injected plasma forms afat z-pinch across the gapbetween the electrodes,accelerating towards the axis.

Plasma Injector: Anelectrothermal dischargebetween two circularrings or sets of annularsegments of ablator.

OuterCylindricalElectrode

InnerElectrode

AnnularRing of

ElectrothermalInjectors A

B

C

D

E

F

G

-

+

-

+

-

+

-

+

Angled injection works nicely.

Right angle turn is too sharp!

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Combining Thio’s new physics approach with contoured gap elecrodes allowedus to produce a small plasma gun that accelerates 1-2 orders of magnitudemore mass to high velocity than straight classical coax guns of similar size.

Clamping RingPolycarbonate

Clamping BoltFiberglass

Clamping RingAluminum

Outer ElectrodeCopper

Inner ElectrodeCopper

Capillary RingKynar

Capillary

Discharge NozzleUHMW Poly

Breakthrough performance achieved

• 90-100 km/s

• 100-350 µg

• 1015 cm−3

• modest current (< 300 kA)

• 32 ablative capillaries (CH2)-100

-50

0

50

100

150

0 10 20 30 40

Cur

rent

(ki

loam

pere

s)

Time (microseconds)

25 ns gate 1 µs gateLow jitter

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F.D. Witherspoon, A. Case, S. J. Messer, R. Bomgardner III,M. W. Phillips, S. Brockington, and R. Elton, “A Contoured GapCoaxial Plasma Gun with Injected Plasma Armature,” Rev. Sci. Inst.80, 083506 (2009).

A. Case, S. Messer, R. Bomgardner, and F. D. Witherspoon, “Inter-ferometer density measurements of a high-velocity plasmoid,” Physicsof Plasmas 17, 053503 (2010).

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The TwoPi test fixtures taught us how to drive and trigger 64 capillaries withlow jitter, in addition to early demonstrations of 2D imploding plasma liners.

Original TwoPi Upgraded TwoPi

(a)

(b) (c)

• Highly symmetric implosion at80 km/s

• Small well defined central

‘sphere’ of high density plasma

• Slower more massive shell fol-

lows later

• Finally collapses/implodes

• Images contrast enhanced to

show detail

Position ne (cm−3) Te (eV )

periphery 2.4× 1014 2.4center 2.5× 1015 4.0center* 1.1× 1017 n/a∗vertically confined

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Modeling for the PLX project, and PJMIF in general, showed it was moreeffective to use much larger masses but at only about ∼50-60 km/s to formthe converging plasma liner.

• Want high-Z gases =⇒ high Mach numbers

• Need high density injection

• Want independent control of mass, veloc-ity, temperature, size

• Need high total mass

• Need straightforward repetitive operation

• Need compact armature injection intocoax gun breech

• Small parallel-plate railguns (Minirail-guns) can provide the needed injector

functionality.

Modeling by UAH and LANL indicated we neededthe following to achieve the 0.1Mbar PLX goal:

• 30 plasma guns

• 8000 µg

• 50 km/s

• 1016 cm−3

• preferably short compact plasma blobswith fast rising density front

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A small parallel-plate “MiniRailgun” makes a good high-Z, high densityplasma injector. Configurations include ablative and high density gas-fed.

Heuristic model

RailsGas Plenum

Insulator Section

Diaphragm

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i

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 0.05 0.1 0.15 0.2

Den

sity

,kg/m

3

Bore position, m

Density profiles for 1 atm Argon in 1 cm plenum

0 µs20 µs40 µs60 µs80 µs

100 µs150 µs200 µs300 µs

Pulse Heat Gas Stored in Plenum

Restraining Diaphragm Bursts

Initiate Arc after Short Delay

Armature Snowplows and Compresses

Two configurations:

Ablative and Gas-Fed

b b

bb

The initial Minirailgun injector concept evolved into a full-fledged high per-formance plasma gun only 30 cm long chosen for the PLX experiment.

Initial few mm bore size 1cm bore size with ablative capillary injector

Fast gas valve developmentGas Inlet

Gas Plenum

Pre-IonizationChamber

Pre-IonizationElectrode

Soleniod

Flyer Plate

Rail Gun

Rails

Mark1 Mark2

Mark2• upgraded valve - more robust

• double coil

• lightweight Al flyer plate

• 60 psi

• > 10 mg Ar

b b

bb

QuadJet experiment first demonstrated higher energy merging of 4 MiniRail-guns with low jitter. Densities 10-100 times higher than previous TwoPi.

Ablative capillary injection into1cm Minirailguns

Nikon D70s open shutter photos (f/29)

With 0.9 Neutral Density Filter

Single MiniRail Stark Density Tein bore 8·1018-2·1019 6eV

at muzzle exit 1·1017 4eVat nozzle exit 2·1016 –

at center 5·1015 3eV

4 MiniRails

Converged

at center 1·1017 5eV

b b

bb

Top and side views reveal “spherical” structure despite only 4 jets

Top view Side view

6 µs after rail trig85 km/s

10 µs after rail trig85 km/s

All PImax photos, 25 ns gate (f/16)

Vertical “polar” jets(Nikon open shutter)

Just beforeinitial collision

b b

bb

The three jet and six jet merge testing at HyperV using argon injected 1 cmguns provided a testbed for demonstrating all required functionality for a 6-gun grouping for PLX.

b b

bb

Fast and open shutter imaging of three and six jets merging shows the sym-metry of convergence and a much denser combined jet.

PI-Max image (5 ns gate) of three merging jets,showng formation of a secondary jet as the plasmaflows past the point of convergence, where it im-pinges on the pressure probe array. [Case 2013]

Six jets mergingthree from each end.

b b

bb

Mark1 guns increased energy and mass over the 1cm. Two Mark1’s were in-stalled on PLX while a higher performing Mark2 version was being developedat HyperV.

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The Mark2 substantially exceeded the PLX plasma gun performance goal of8000 µg at 50 km/s (achieved with ∼500 kA).

700 kA sparkgap switch

Although this performance is already in the

ballpark for that needed for a reactor-grade

plasma gun driver, i.e. 10-20 mg at 50-70 km/s,

we want more than just mass and velocity!

PLX/PJMIF Land!!

b b

bb

We also need plasma jet shape control for a reactor driver

• The coax geometry along with nozzles gives better control of jet topology

• Want a jet structure more like a pancake/hocky puck instead of a fat cigar

• Lower current density of coax gun reduces electrode erosion and impurities

CL

-

+

7.8 µs4.3×1016 cm−3

190 k/s

CL

-

+

7.8 µs2.15×1016 cm−3

195 k/s

CL

-

+

7.8 µs1.11×1016 cm−3

205 k/s

b b

bb

Simulations show that contoured-gap coaxial plasma guns can indeed accel-erate the required masses to the required velocities. The task is to minimizetheir size and cost and increase efficiency.

89 cm

49 cm

20 cm

30 cm

26 cm

8 cm

Scale

Full

Half

CL

-

+

CL

-

+

CL

-

+

CL

-

+

CL

-

+

CL

-

+

CL

-

+

Mach2 Simulations Predict HighMass/Density Capability

200-400 µg at 200 km/s for 800 kA8000 µg at 50 km/s for 800 kA

0

2

4

6

8

10

12

14

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 150

50

100

150

200

250

Ener

gy

(kJ),

Curr

ent

(105

Am

ps)

Vel

oci

ty,km

/s

Time, microsec

VbulkEkinetic

EmagneticEjoule

Current

(b)

b b

bb

Contoured gap coax + Minirailgun injectors ⇒ Reactor-grade driver

• Eliminates linear insulator - reduces high velocity plasma/wall interactions

• Lower current density reduces impurities and electrode erosion

• Better shaping of plasma jet/blob - better symmetry, superior jet topology

(and easier to control)

• Easier to implement a structured armature

• Lower lead inductance (matched pfn ⇒ high efficiency, no ringing)

• Electrodes act as own vacuum containment – much simpler vacuum and

mounting design

b b

bb

A reactor-grade plasma gun uses an array of small gas-fed Minirailgun injec-tors and an integrated well-matched pulse forming network.

Gas Inlet

Gas Plenum

Pre-Ionization

Chamber

Pre-Ionization

Electrode

Soleniod

Flyer Plate

Rail Gun

Rails

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Integrated Pulse Forming Network

PFN Module 1

Module 2

Module 3

Module 4Gun

Gas Inlet

Gas Plenum

Pre-Ionization

Chamber

Pre-Ionization

Electrode

Soleniod

Flyer Plate

Rail Gun

Rails

Minirailgun Injector Array

Symmetrical low inductance current feeds

20km

/s

50-60 km/sXe

Injectors not to scale!qty ∼ 24

Early example of an integratedgun/RLC package.

• 50 kJ per gun

• 0.5m length

• 5-7 cm jet radius

• 10-20 mg at 50-60 km/s

• 1 Hz reprate

• Refractory materials

• Switchless - if possible

• 50-80% efficiency

• $10-20K per gun modulein production quantities

• 30M shot lifetime

• $0.02/MJ over lifetime

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A Pulse Forming Network can be matched to a low impedance coax gun byarranging the pfn wave speed to match the armature velocity profile.

Assume constant acceleration

a =v2

2x=

(60 k/s)2

2(0.5 m)= 3.6 · 109m/s2 (1)

For a railgun,

F = ma =1

2L′gI

2 (2)

so that for m= 10 mg and L′g = 0.138 µH/m

I = (2ma

L′g)1/2 = 722 kA (3)

and the acceleration time is

taccel = (2x

a)1/2 = 16.7 µs. (4)

The pulse width of a pfn is given by

τ = 2CZ ≃ 2CL′g〈v〉 (5)

where we have matched the impedance of the pfn tothat of the gun.

Z ≃ L′g〈v〉 ≃ 0.004 (6)

Thus,

C =τ

2L′g〈v〉= 0.002 F (7)

Z =

√

L′

C ′=

√

L

C(8)

L = CZ2 = 32nH (9)

A quick circuit simulation of only a four section pfn witheach C=500 µF and each L = 8 nH. Charge voltage is5 kV. This pfn needs tweaking but shows a fairly wellmatched pfn to the load. A real system might have 9or more sections.

A matched gun and pfn should allow

electrical efficiencies of 50-80%.

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Issues and Challenges

• Determining proper electrode contour gap. Parameter space is very large.

We need to characterize parameter space and identify those regions best

suited for the required performance.

• Developing robust injector system – fast gas valves with long life

• Demonstrating high efficiency, >50%

• Repetitive pulsed power systems

• Demonstrating compact structured jets with proper topology

• Integrated PFN-plasma gun driver

• Switchless operation (fallback is solid-state)

• Maintaining low jitter over hundreds of guns

• Achieving projected costs

• Low cost manufacturing guns in mass produced quantities

• Robust - must survive fusion blast

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References

• Burton, R. L. and P. J. Turchi, “Pulsed plasma thruster,” Journal of Propulsion and Power, 14(5):716735(1998).

• Case, A., S. Messer, S. Brockington, L. Wu, F.D. Witherspoon, R. Elton, “Merging of high speed argonplasma jets,” Physics of Plasmas 20, 012704 (2013).

• A. Case, S. Messer, R. Bomgardner, and F. D. Witherspoon, “Interferometer density measurements ofa high-velocity plasmoid,” Physics of Plasmas 17, 053503 (2010).

• Cassibry, J., F. Thio, T. E Markusic, and S. T Wu, “Numerical Modeling of a Pulsed ElectromagneticPlasma Thruster Experiment,” Journal of Propulsion and Power 22 (2): 628636 (2006).

• Cassibry, J., F. Thio, and S. T Wu, “2-D Axisymmetric Magnetohydrodynamic Analysis of Blowby in aCoaxial Plasma Accelerator,” Physics of Plasmas 13 (5) (2006).

• Cassibry, J., M. Stanic, and S. Hsu, “Ideal hydrodynamic scaling relations for a stagnated implodingspherical plasma liner formed by an array of merging plasma jets,” Physics of Plasmas 20, 032706(2013).

• Cheng, D. Y., “Plasma deflagration and the properties of a coaxial plasma deflagration gun,” NuclearFusion, (10):305317 (1970).

• Cheng, D. Y. “Application of a Deflagration Plasma Gun as a Space Propulsion Thruster,” AIAAJournal 9 (9): 16811685 (1971).

• A. Dattner and J. Eninger, “Studies of a coaxial plasma gun,” Physics of Fluids Supplement, 7(11):S41S44(1964).

• Degnan, J. H., W. L. Baker, M. Cowan, J. D. Graham, J. H. Holmes, E. A. Lopez, D. W. Price, D. Ralph,and N. F. Roderick, “Operation of Cylindrical Array of Plasma Guns,” Fusion Technology 35: 354360(1999).

• Gloersen, P., B. Gorowitz, and J. T Kenney, “Energy Efficiency Trends in a Coaxial Gun Plasma EngineSystem,” AIAA Journal 4 (3): 436441 (1966).

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References - cont’d

• D.C. Hagerman and J. E. Osher, “Two high velocity plasma guns,” The Review of Scientific Instruments,34(1):5660 (1963).

• R.G. Jahn, “Physics of Electric Propulsion,” 1st ed., New York, McGraw-Hill (1968).

• Kirkpatrick R. C., C.E. Knapp, Y. C. F. Thio, “Progress in magnetized target fusion driven by plasmaliners,” In E. Panarella, editor, Current Trends in International Fusion Research. Proc. of the 4thSymposium. Physics Essay, Ottawa, Canada (2002).

• Komelkov, V.S., and V.I. Modzolevskii, “Coaxial Accelerator for Dense Plasmas,” Soviet Journal ofPlasma Physics 3 (5): 533538 (1977).

• Lee, J.H., D.R. McFarland, and F. Hohl, “Production of dense plasmas in a hypocycloidal pinch appa-ratus,” Physics of Fluids, 20(2):313321 (1977).

• John Marshall, “Performance of a hydromagnetic plasma gun,” Physics of Fluids:Letters to the Editor,3(1):134135 (1960).

• J. W. Mather, “Investigation of the high-energy acceleration mode in the coaxial gun,” The Physics ofFluids Supplement, 7(11):S28S34 (1964).

• Merritt, E.C., A.L. Moser, S.C. Hsu, J. Loverich, and M. Gilmore, “Experimental Characterization ofthe Stagnation Layer between Two Obliquely Merging Supersonic Plasma Jets,” Phys. Rev. Lett. 111,085003 (2013).

• Thio, Y. C. F., C. E. Knapp, R. C. Kirkpatrick, R. E. Siemon, and P. J. Turchi, “A physics exploratoryexperiment on plasma liner formation,” Journal Fusion Energy, 20(1/2):111 (2001).

• Thio, Y. C., “Status of the U. S. Program in Magneto-inertial Fusion,” Journal of Physics: ConferenceSeries 112 (042084) (1978).

• Thio, Y. C. F, J. T. Cassibry, and T. E. Markusic, “Pulsed Electromagnetic Acceleration of Plasmas,” In38th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit. Indianapolis, Indiana (2002).

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References - cont’d

• Y. C. F. Thio, E. Panarella, R. C. Kirkpatrick, C. E. Knapp, and F. Wysocki, “Magnetized target fusionin a spheroidal geometry with standoff drivers,” In E. Panarella, editor, Current Trends in InternationalFusion Research Proceedings of the Second Symposium, Ottawa, Canada, NRC Research Press (1999).

• Turchi, P. J, and J. F. Davis, “Propagation of Dense Plasma Jets,” In SPIE Microwave and ParticleBeam Sources and Propagation. Vol. 873. Los Angeles, California (1988).

• Witherspoon, F. D. A. Case, S. J. Messer, R. Bomgardner III, M. W. Phillips, S. Brockington, and R.Elton, “A Contoured Gap Coaxial Plasma Gun with Injected Plasma Armature,” Rev. Sci. Inst. 80,083506 (2009).

• J. K. Ziemer, “Performance Scaling of Gas-Fed Pulsed Plasma Thrusters,” Phd dissertation, PrincetonUniversity, 2001.